Lets define A(x) to be the average cost function where A(x) = C(x)/x basically you divide the given cost function C(x) by the number of units produced (x)
Dividing C(x) over x leads to: A(x) = C(x)/x A(x) = (14000+94x+0.03x^2)/x ... substitution A(x) = (0.03x^2+94x+14000)/x ... rearrange terms A(x) = (0.03x^2)/x+(94x)/x+(14000)/x ... break up the fraction A(x) = 0.03x + 94 + (14000/x) ... simplify
If x were to head off to infinity, then the portion 14000/x approaches 0.
So this is why the oblique asymptote is y = 0.03x + 94
Basically, in the long run, the average cost will approach y = 0.03x + 94
